Banks have started taking roundabout methods of trying to compete with money market mutual funds for deposits through credit-card companies and subsidiaries, although they are prohibited by law from directly setting up their own funds.

Visa USA -- provoked by its rival, American Express Co., which recently revealed plans to take over the brokerage firm Shearson Loeb Rhoades and its money fund -- announced it would provide a product that would be "fully competitive both with travel and entertainment cards and money market funds."

According to Visa USA President Charles T. Russell, the card would enable customers to "access funds on deposit in an account which invests in high-yield financial instruments and possibly give them access to the value held in other assets, as well."

Russell did not give details, but industry sources speculated that the product could work in the following manner. Visa cards now are issued by 14,000 member banks and thrift institutions. Customer accounts would be established at a new or existing money market fund through the issuing banks.

Because banks are prohibited by law from running money market funds, the operation of the fund would be independent of the banks. Credit card companies like Visa are under no such restrictions. However, the fund trustees could be expected to purchase certificates of deposit from the member banks, provided their rates were competitive with other investments. Visa hopes to offer this product by the end of the year.

A variation on this theme is being developed by Ronald Randall of Stamford, Conn. Randall, whose specialty is data-processing, has signed up eight regional banks for his UniFinancial Service project. They include the Marine Midland of Buffalo and, in this area, First and Merchants of Richmond and Maryland National Bank in Baltimore.

The object is to stop the hemorrhaging of bank funds to money market funds by making banks the center of the funds management program of each customer. For a monthly fee of between $5 and $10, a customer would get a combined financial statement showing checking, savings and credit card balances, mortgage payments, home equity and other transactions. At the same time, the bank would channel the customer's money into a money market fund.

From the customer's viewpoint, the yield would be the same as offered by any money market fund. The principal would not be insured. The bank, in turn, would retain the customer for other services, make money off the monthly fee and, it is hoped, retain some of its funds in the form of bank certificates of deposit purchased by the money market fund.

Earlier this year, the Federal Reserve stopped Citicorp from offering market rates on its new Choice Card account. A week ago Citicorp began soliciting its credit card customers, offering them six-month certificates of deposit yielding 14 percent on a minimum $3,000 investment. This is a variation of the "loophole" certificate, in which Citicorp "lends" the customer another $7,000, but Citicorp will allow customers to write checks on that $7,000.

Manufacturers Hanover and Chase Manhattan also announced new market rate certificates of deposit to be issued through their subsidiaries.

Federal banking regulators have not yet commented on these latest schemes to get around the prohibition against banks offering market rates.

Equitable Life Assurance Society also said it will be among the latest competitors for U.S. cash.

Equitable has applied to the New York State Insurance Department for authority to offer a broad cash-management system to corporate customers seeking short-term, high-interest investments traditionally offered only by banks, a spokeswoman told the Associated Press.

As of Tuesday, it was estimated that since the beginning of the year, high-interest money market mutual funds offered by non-banks had siphoned away nearly $120 billion from banks, by paying as much as three times the interest banks are permitted to pay for conventional savings.

Money market funds pool investors' money to buy big-denomination certificates of deposit, the interest on which is not regulated. The funds -- which banks are barred from offering -- also allow investors to withdraw money whenever they wish, a feature not available to individual purchasers of certificates of deposit.

Citicorp, the nation's biggest bank holding company, said Tuesday it began a mailing April 22 to 150,000 of its credit card customers in 15 states offering 14 percent interest on $3,000-minimum certificates of deposit.

If responses to the test mailing is sufficient, Citicorp plans a nationwide campaign for consumer deposits.

Chase Manhattan Corp., owner of the third-largest bank in the nation, ran ads in Miami in early April seeking deposits in New York and in a Florida bank it plans to open, but no decision has been made whether to renew the campaign, a spokesman said.

Manufacturers Hanover Corp., ranked No. 4 in the nation, is planning to offer small denomination investment certificates to consumers at "market rates of interest," higher than customary bank interest rates, through its 442 consumer finance offices in 25 states.

Equitable's campaign, still in the formative stages, will not be spelled out until it is approved by the state, according to the spokeswoman.